saddlecloth

noun, plural sad·dle·cloths [sad-l-klawth z, -kloth z, -klawths, -kloths] /ˈsæd lˌklɔðz, -ˌklɒðz, -ˌklɔθs, -ˌklɒθs/.

1. Horse Racing. a cloth placed over the saddle of a racehorse bearing the horse’s number.
2. saddle blanket.

noun

1. a light cloth put under a horse’s saddle, so as to prevent rubbing